Hi Stephen,
Every species may have different requirements for chill hours or various other aspects of seed stratification. So it's best to research each berry varietie individually for necessary steps in stratification then germination. A simple
online search from the search engine of your choice
should reveal good results with 15 minutes of studying each species you're interested in. You'll just want to make sure you're collecting seeds from good heirloom varieties known to be true to type or if there will be cross polination from multiple varieties, understand it may decrease the chances of getting similarly producing stock.
The types of genetics you're dealing with in many if not most types of bushes require a polinator and if I'm not mistaken they are diploid, and not self fertile, like most blueberries for example. This means each seed will create its own unique variety which may or may not have desirable characteristics. Think of it like playing the lottery. If you have the time and space to grow a thousand bushes, and access to desirable parent stock for berry picking. After many years of growing your seedlings, you may have the next big hit for optimal berry production of precocious and fruit heavy, tasty large berries.
My personal recommendation is getting starts. Most raspberry owners have a runaway issue, so digging early spring side shoots escaping the area is often just annual maintenence in
yard settings. Runners from strawberries can be an issue escaping beds, and even just one runner in early spring, can have numerous new plants started by runners before fall, depending on how vigorous the variety is. Then for other bushes like blueberries, taking cuttings will get you a tried and true variety.
I've seen some success with starting from seed with some varieties, and wild or invasive blackberries seem true to seed. So may some raspberries, but many species just don't do as well regarding producing consistently productive offspring. Which is why cloning, grafting and rooting are such widespread and commonly used practices in horticulture. When you look at those who are set up to have success finding productive varieties from seed in diploid seed propagation, they often are growing a thousand seeds to size, to begin decent fruit production, then after proper evaluation sometimes only have a few worthy varieties worth naming for use.
Hope that helps!